I'm not sure I understand, I think this definition still works for left outer joins on conditions other than identity equality, since joins on, say, inequalities or multiple conditions would still be "guaranteed to keep all rows from the first (left) table. Columns from the right table are filled with....".
It kind of implies that the left join process works by first taking the left table and then filling in the right table with a match if one exists, and otherwise null.
That model obviously doesn't work because if there's more than one match as the matching left row is duplicated for each match. However I don't understand their point of this being a problem when you don't have a "identity equality join condition", since this can also occur for equality joins as long as you're not joining on a unique key.
